Every words stands for unique digit that makes the arithmetic equation true

SEVEN + SEVEN + SIX = TWENTY.

What are the digits ?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

I am lying and I always lie. Tell me whether I am lying or telling the truth.

How can you write nineteen in a manner that if we take out one, it becomes twenty?

A certain street contains 100 buildings. They are numbered from 1 to 100. How many 9's are used in these numbers?

What number should come in place of the question mark below?

On her drawing table, Sayna lit 12 coloured candles. A few seconds later she blew two candles off.

How many candles Sayna have at the end?

Wednesday, Steve and Pam go to a restaurant to eat lunch. After eating lunch, they pay the bill. But Steve and Pam do not pay the bill. So…who does?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

I am eight letters long - "12345678"
My 1234 is an atmospheric condition.
My 34567 supports a plant.
My 4567 is too appropriate.
My 45 is a friendly thank-you.
My 678 is a man's name.

What word am I?